The ideal MHD equation of motion is We will now prove that the ideal MHD force operator F{ξ} is self-adjoint.1 That is, we will demonstrate that for any two vector fields ξ and η satisfying the same boundary conditions, Proof The total energy of the system is We have seen that this quantity is conserved in ideal MHD, so that Here, K is the kinetic energy and δW is the change in the potential energy of the system, as a result of the displacement.
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© 2009 Springer-Verlag Berlin Heidelberg
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Schnack, D.D. (2009). Proof that the Ideal MHD Force Operator is Self-Adjoint. In: Lectures in Magnetohydrodynamics. Lecture Notes in Physics, vol 780. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-00688-3_22
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DOI: https://doi.org/10.1007/978-3-642-00688-3_22
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